Q-Rung Interval-Valued Probabilistic Dual Hesitant Fuzzy Sets: A New Tool for Multiattribute Group Decision-Making

This paper aims at proposing a novel multiattribute group decision-making (MAGDM) method in complex decision-making environments. To this end, we first introduce a tool, called q-rung interval-valued probabilistic dual hesitant fuzzy sets (q-RIVPDHFSs), for decision makers to express their evaluation information over a set of finite alternatives in MAGDM procedures. The q-RIVPDHFS consists of some possible membership and nonmembership degrees, along with their interval-valued probabilistic information. Due to this structure, q-RIVPDHFSs are more powerful and flexible than the traditional q-rung probabilistic q-rung dual hesitant fuzzy sets, in which probabilistic information of membership and nonmembership degree is denoted by crisp numbers. Second, some other related concepts of q-RIVPDHFSs, such as operational laws, comparison method, distance measure, and aggregation operators, are introduced. Third, based on these novel concepts, two MAGDM methods (Algorithms 1 and 2) are put forward. Last but not least, a practical decision-making example is provided to show the effectiveness of our proposed MAGDM method. We also compare our Algorithms 1 and 2 with some existing decision-making methods to explain why our methods are more powerful and useful.